Find the expression that is equivalent to $\frac{\tan \frac{3 π}{4} + \tan \frac{π}{6}}{1 - \tan \frac{3 π}{4} \tan \frac{π}{6}}$ .
Choose the correct answer below.
A. $\tan \frac{7 π}{12}$
B. $\tan \frac{π}{8}$
c. $\tan \frac{11 π}{12}$
D. $\tan \frac{3 π}{4} + \tan \frac{π}{6}$

Answer

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Answer

So, the correct answer is $C . \tan \frac{11 π}{12}$

Steps

Step 1 ：The given expression is $\frac{\tan \frac{3 π}{4} + \tan \frac{π}{6}}{1 - \tan \frac{3 π}{4} \tan \frac{π}{6}}$

Step 2 ：This expression is in the form of the tangent addition formula, which is $\tan (a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}$

Step 3 ：Here, $a = \frac{3 π}{4}$ and $b = \frac{π}{6}$

Step 4 ：So, the expression is equivalent to $\tan (a + b)$ , which is $\tan (\frac{3 π}{4} + \frac{π}{6})$

Step 5 ：Adding the values of a and b, we get $\frac{3 π}{4} + \frac{π}{6} = \frac{11 π}{12}$

Step 6 ：Final Answer: The expression is equivalent to $\tan \frac{11 π}{12}$

Step 7 ：So, the correct answer is $C . \tan \frac{11 π}{12}$